Finite Group Databasebeta

← #11906388

Subgroups — #11906388

Order 1152.

2231 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596049C211yesmaximal, characteristic, complemented
2C3×#5579C211yesmaximal, characteristic, complemented
3C3×Q8×Dic6C211yesmaximal, characteristic, complemented
4#10595371C212yesmaximal, complemented
5#10595367C212yesmaximal, complemented
6#10594537C212yesmaximal, complemented
7#10594391C214yesmaximal, complemented
8#10594378C214yesmaximal, complemented
9D3×#888C212yesmaximal, complemented
10#10593956C211yesmaximal, characteristic, complemented
11#10593909C211yesmaximal, characteristic, complemented
12#10593904C212yesmaximal, complemented
13#10593889C212yesmaximal
14C4×#3796C211yesmaximal, characteristic
15#10593856C211yesmaximal, characteristic, complemented
16#10593855C212yesmaximal, complemented
17#10593853C212yesmaximal, complemented
18#87041—31nomaximal
19#86926—31nomaximal
20C2×#3797C2212yes—
21C2×#3796C2211yescharacteristic
22C2×D3×Dic6C2214yes—
23C32×C4×Q8C2211yescharacteristic
24#64155C2211yescharacteristic
25#64153C2211yescharacteristic
26#64106C2211yescharacteristic
27#64105C2212yes—
28#64098C2212yes—
29#64097C2211yescharacteristic
30#64081C2212yes—
31C42×C3⋊D3C2211yescharacteristic
32C4×#634C2212yes—
33C4×#634C2211yescharacteristic
34C3×#946C2212yes—
35C3×Q8×Dic3C2212yes—
36C3×#896C2214yes—
37C3×D3×C4⋊C4C2212yes—
38C3×#888C2212yes—
39C3×#888C2214yes—
40C3×C4×D12C2211yescharacteristic
41C3×C4×D12C2212yes—
42C3×#870C2212yes—
43C3×#869C2212yes—
44C3×#869C2211yescharacteristic
45C3×#869C2211yescharacteristic
46C3×C4×Dic6C2212yes—
47C3×C4×Dic6C2211yescharacteristic
48#63919C2212yes—
49#63919C2212yes—
50#63919C2212yes—
51#63918C2212yes—
52#63904C2214yes—
53C4×#626C2212yes—
54#63900C2212yes—
55#63900C2212yes—
56#63899C2214yes—
57#63899C2214yes—
58#63898C2211yescharacteristic
59#63898C2212yes—
60#63895C2214yes—
61D3×C4⋊Dic3C2212yes—
62#63888C2214yes—
63#63887C2214yes—
64#63881C2212yes—
65#63880C2214yes—
66#63878C2212yes—
67#63877C2214yes—
68D3×Dic3⋊C4C2214yes—
69C4×D3×Dic3C2212yes—
70#63873C2212yes—
71#63872C2212yes—
72#63867C2214yes—
73#63857C2212yes—
74#63856C2214yes—
75#63849C2211yescharacteristic
76#63847C2214yes—
77#63845C2214yes—
78#63844C2212yes—
79#63843C2211yescharacteristic
80#63843C2212yes—
81#63840C2214yes—
82#63839C2214yes—
83#63839C2214yes—
84#63837C2214yes—
85C3×Q82—31no—
86C3×#554—31no—
87#5730—32no—
88#5730—31no—
89#5729—34no—
90#5729—32no—
91#5727—34no—
92#5727—32no—
93D3×C4⋊Q8—32no—
94D3×C4⋊Q8—31no—
95D3×C4⋊Q8—31no—
96#5722—31no—
97#5689—32no—
98#5685—32no—
99#5635—32no—
100#5632—34no—
101#5623—34no—
102#5622—32no—
103#5579—32no—
104#5579D311yescharacteristic, complemented
105#5578—31no—
106#5578—31no—
107#5578—32no—
108#5578—61no—
109#5574—32no—
110C4×#239—31no—
111#5569—32no—
112Q8×Dic6—31no—
113Q8×Dic6D311yescharacteristic, complemented
114#5546—32no—
115#5543—31no—
116D4×Dic6—32no—
117C4×#237—31no—
118#5511—32no—
119C2×#888—32no—
120C2×C32×Q8C2311yescharacteristic
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×#634C2312yes—
125C2×#634C2311yescharacteristic
126C2×C3×D12C2311yescharacteristic
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2314yes—
129C2×C3×Dic6C2314yes—
130C2×C3×Dic6C2312yes—
131C2×C3×Dic6C2312yes—
132C2×C3×Dic6C2311yescharacteristic
133C2×#627C2314yes—
134C2×#627C2314yes—
135C2×#626C2312yes—
136C2×#624C2314yes—
137C2×D3×Dic3C2312yes—
138C2×D3×Dic3C2314yes—
139C2×D3×Dic3C2312yes—
140#3797—44no—
141#3796Q818yescomplemented
142D3×Dic6—48no—
143C32×C4⋊C4C2311yescharacteristic
144C32×C4⋊C4C2312yes—
145C32×C42C2311yescharacteristic
146C32×C42C2312yes—
147#3752C2312yes—
148#3752C2312yes—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150C4⋊(C3⋊Dic3)C2312yes—
151#3750C2312yes—
152#3750C2312yes—
153#3750C2312yes—
154#3750C2312yes—
155#3750C2312yes—
156C4×C3⋊Dic3C2311yescharacteristic
157C4×C3⋊Dic3C2312yes—
158C4×C3⋊Dic3C2311yescharacteristic
159C4×C3⋊Dic3C2311yescharacteristic
160C3×(C2×D3)⋊C4C2312yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×C4⋊Dic3C2314yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2311yescharacteristic
168C3×C4⋊Dic3C2312yes—
169C3×Dic3⋊C4C2312yes—
170C3×Dic3⋊C4C2314yes—
171C3×Dic3⋊C4C2314yes—
172C3×Dic3⋊C4C2314yes—
173C3×C4×Dic3C2314yes—
174C3×C4×Dic3C2312yes—
175#3724C2314yes—
176#3724C2314yes—
177#3724C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2312yes—
182#3722C2312yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2314yes—
185Dic32C2312yes—
186Dic32C2314yes—
187Dic32C2312yes—
188#3503—91noSylow
189C2×#239—31no—
190C2×D3×Q8—34no—
191C2×D3×Q8—32no—
192C2×D3×Q8—32no—
193C2×#237—31no—
194C22×Dic6—34no—
195C3×C4⋊Q8—32no—
196C3×C4⋊Q8—34no—
197C3×C4⋊Q8—31no—
198C3×C4⋊Q8—32no—
199C3×C4⋊Q8—31no—
200C3×#125—32no—
201C3×C22⋊Q8—32no—
202C3×C22⋊Q8—34no—
203C3×C4×Q8—21no—
204C3×C4×Q8—32no—
205C3×C4×Q8—31no—
206C3×C4×Q8—32no—
207C3×C4×Q8C2×D311yescharacteristic
208C3×C4×Q8C2×D311yescharacteristic
209C3×C4×D4—31no—
210C3×C4×D4—32no—
211C2×C3×C4⋊C4—32no—
212#946—31no—
213#946—31no—
214#946—34no—
215#946—34no—
216#946—34no—
217#946—61no—
218#946C2×D312yes—
219Q8×Dic3—32no—
220Q8×Dic3—31no—
221Q8×Dic3C2×D312yes—
222#944—31no—
223#944—31no—
224#944—32no—
225#944—32no—
226#944—34no—
227#944—34no—
228#944—61no—
229D4×Dic3—31no—
230D4×Dic3—32no—
231C4×#67—34no—
232C4×#67—32no—
233C2×C4⋊Dic3—32no—
234#924—34no—
235#924—32no—
236C2×Dic3⋊C4—34no—
237C2×C4×Dic3—32no—
238#897—32no—
239#897—31no—
240#897—31no—
241#897—34no—
242#897—61no—
243#896—34no—
244#896—32no—
245#896—32no—
246#896—34no—
247#896—34no—
248#896—34no—
249#896—62no—
250#896C2×D314yes—
251#893—31no—
252#893—32no—
253#893—34no—
254#893—32no—
255#892—32no—
256#892—31no—
257#892—31no—
258D3×C4⋊C4—34no—
259D3×C4⋊C4—32no—
260D3×C4⋊C4—32no—
261D3×C4⋊C4—32no—
262D3×C4⋊C4—32no—
263D3×C4⋊C4—32no—
264D3×C4⋊C4C2×D312yes—
265#890—32no—
266#890—32no—
267#890—34no—
268#889—32no—
269#889—32no—
270#889—34no—
271#889—34no—
272#889—34no—
273#889—34no—
274#889—62no—
275#888—34no—
276#888—34no—
277#888—31no—
278#888—31no—
279#888—32no—
280#888—32no—
281#888—32no—
282#888—32no—
283#888—32no—
284#888—32no—
285#888—34no—
286#888—34no—
287#888—32no—
288#888—61no—
289#888C2×D314yes—
290#888C2×D312yes—
291#887—31no—
292#887—32no—
293#887—34no—
294#887—32no—
295#67⋊C4—32no—
296#67⋊C4—34no—
297#878—34no—
298#878—34no—
299#878—34no—
300#877—32no—
301#877—34no—
302C4×D12—32no—
303C4×D12—34no—
304C4×D12C2×D312yes—
305C4×D12C2×D311yescharacteristic
306#872—32no—
307#872—32no—
308#872—34no—
309#872—62no—
310C42×D3—32no—
311C42×D3—31no—
312C42×D3—31no—
313C42×D3—61no—
314#870—34no—
315#870C2×D312yes—
316#869—32no—
317#869C2×D312yes—
318#869C2×D311yescharacteristic
319#869C2×D311yescharacteristic
320C4×Dic6—32no—
321C4×Dic6—31no—
322C4×Dic6—32no—
323C4×Dic6—31no—
324C4×Dic6—32no—
325C4×Dic6—34no—
326C4×Dic6—62no—
327C4×Dic6—61no—
328C4×Dic6C2×D312yes—
329C4×Dic6C2×D311yescharacteristic
330C22×C3⋊D3C2411yescharacteristic
331C22×C3×D3C2412yes—
332C32×Q8—22no—
333C2×C32×C4C2412yes—
334C2×C32×C4C2412yes—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2411yescharacteristic
338C2×C3⋊Dic3C2412yes—
339C2×C3⋊Dic3C2411yescharacteristic
340C2×C3⋊Dic3C2412yes—
341C2×C3⋊Dic3C2411yescharacteristic
342C2×C3⋊Dic3C2411yescharacteristic
343C4×C3⋊D3—22no—
344C4×C3⋊D3—22no—
345C4×C3⋊D3C2×Q814yescomplemented
346#634—22no—
347#634—24no—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2414yes—
351C2×C3×Dic3C2414yes—
352C2×C3×Dic3C2412yes—
353C3×D12C2×Q814yescomplemented
354C3×C4×D3—24no—
355C3×C4×D3—44no—
356C3×Dic6—44no—
357C3×Dic6—42no—
358C3×Dic6—42no—
359C3×Dic6C2×Q814yescomplemented
360#627—28no—
361#627—44no—
362#626C2×Q818yescomplemented
363#624—44no—
364D3×Dic3—24no—
365D3×Dic3—44no—
366D3×Dic3C2×Q818yescomplemented
367Q82—31no—
368Q82—91no—
369#557—92no—
370#554—31no—
371#554—92no—
372#554—91no—
373#554—92no—
374D4×Q8—92no—
375D4×Q8—94no—
376#544—94no—
377#544—92no—
378#533—92no—
379#533—91no—
380C2×C4⋊Q8—92no—
381C2×C4⋊Q8—91no—
382#520—92no—
383C4×#41—91no—
384C2×C3×Q8—21no—
385C2×C3×Q8—31no—
386C2×C3×Q8—32no—
387C2×C3×Q8—34no—
388C2×C3×Q8—32no—
389C2×C3×Q8C22×D311yescharacteristic
390C2×C3×Q8C22×D311yescharacteristic
391C2×C3×D4—31no—
392C22×C3×C4—32no—
393C22×C3×C4—34no—
394C2×#67—32no—
395C22×Dic3—32no—
396C22×Dic3—32no—
397C22×Dic3—34no—
398#239—38no—
399D3×Q8—124no—
400D3×Q8—124no—
401D3×Q8—128no—
402#237—38no—
403C2×D12—32no—
404C2×D12C22×D311yescharacteristic
405C2×C4×D3—32no—
406C2×C4×D3—31no—
407C2×C4×D3—31no—
408C2×C4×D3—32no—
409C2×C4×D3—31no—
410C2×C4×D3—31no—
411C2×C4×D3—31no—
412C2×C4×D3—31no—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—61no—
417C2×C4×D3—61no—
418C2×C4×D3—61no—
419C2×C4×D3C22×D312yes—
420C2×C4×D3C22×D314yes—
421C2×Dic6—31no—
422C2×Dic6—31no—
423C2×Dic6—32no—
424C2×Dic6—32no—
425C2×Dic6—34no—
426C2×Dic6—34no—
427C2×Dic6—34no—
428C2×Dic6—34no—
429C2×Dic6—62no—
430C2×Dic6—61no—
431C2×Dic6—128no—
432C2×Dic6C22×D312yes—
433C2×Dic6C22×D312yes—
434C2×Dic6C22×D314yes—
435C2×Dic6C22×D311yescharacteristic
436C3×C4⋊C4—21no—
437C3×C4⋊C4—22no—
438C3×C4⋊C4—32no—
439C3×C4⋊C4—32no—
440C3×C4⋊C4—34no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—34no—
443C3×C4⋊C4—32no—
444C3×C4⋊C4—31no—
445C3×C4⋊C4—34no—
446C3×C4⋊C4—32no—
447C3×C4⋊C4—32no—
448C3×C4⋊C4—34no—
449C3×C4⋊C4C22×D311yescharacteristic
450C3×C4⋊C4C22×D311yescharacteristic
451C3×C4⋊C4C22×D312yes—
452C3×C4⋊C4C22×D312yes—
453C3×C22⋊C4—32no—
454C3×C22⋊C4—34no—
455C3×C42—21no—
456C3×C42—22no—
457C3×C42—32no—
458C3×C42—34no—
459C3×C42C22×D311yescharacteristic
460C3×C42C22×D312yes—
461C3×C42C22×D311yescharacteristic
462C3×C42C22×D312yes—
463#217—34no—
464#217—32no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—32no—
467(C2×D3)⋊C4—32no—
468(C2×D3)⋊C4—32no—
469(C2×D3)⋊C4—32no—
470(C2×D3)⋊C4—32no—
471(C2×D3)⋊C4—32no—
472(C2×D3)⋊C4—32no—
473(C2×D3)⋊C4—62no—
474(C2×D3)⋊C4—62no—
475(C2×D3)⋊C4C22×D314yes—
476(C2×D3)⋊C4C22×D312yes—
477C4⋊Dic3—31no—
478C4⋊Dic3—31no—
479C4⋊Dic3—32no—
480C4⋊Dic3—32no—
481C4⋊Dic3—34no—
482C4⋊Dic3—34no—
483C4⋊Dic3—32no—
484C4⋊Dic3—34no—
485C4⋊Dic3—61no—
486C4⋊Dic3—62no—
487C4⋊Dic3C22×D312yes—
488C4⋊Dic3C22×D311yescharacteristic
489C4⋊Dic3C22×D312yes—
490C4⋊Dic3C22×D312yes—
491C4⋊Dic3C22×D314yes—
492C4⋊Dic3C22×D312yes—
493C4⋊Dic3C22×D311yescharacteristic
494Dic3⋊C4—32no—
495Dic3⋊C4—32no—
496Dic3⋊C4—32no—
497Dic3⋊C4—32no—
498Dic3⋊C4—32no—
499Dic3⋊C4—32no—
500Dic3⋊C4—32no—
501Dic3⋊C4—32no—
502Dic3⋊C4—32no—
503Dic3⋊C4—32no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—32no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—62no—
515Dic3⋊C4—62no—
516Dic3⋊C4—62no—
517Dic3⋊C4—62no—
518Dic3⋊C4—62no—
519Dic3⋊C4C22×D314yes—
520Dic3⋊C4C22×D312yes—
521Dic3⋊C4C22×D314yes—
522Dic3⋊C4C22×D314yes—
523C4×Dic3—31no—
524C4×Dic3—31no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—31no—
528C4×Dic3—31no—
529C4×Dic3—31no—
530C4×Dic3—31no—
531C4×Dic3—32no—
532C4×Dic3—34no—
533C4×Dic3—32no—
534C4×Dic3—34no—
535C4×Dic3—32no—
536C4×Dic3—32no—
537C4×Dic3—61no—
538C4×Dic3—62no—
539C4×Dic3—61no—
540C4×Dic3—61no—
541C4×Dic3C22×D314yes—
542C4×Dic3C22×D312yes—
543C22×C32C2511yescharacteristic
544C2×C3⋊D3—21no—
545C2×C3⋊D3—21no—
546C2×C3⋊D3C22×Q812yes—
547C2×C3×D3—22no—
548C2×C3×D3—22no—
549C2×C3×D3C22×Q814yes—
550C32×C4—21no—
551C32×C4—22no—
552C32×C4—22no—
553C32×C4C22×Q812yes—
554C32×C42−1+412yes—
555C3⋊Dic3—22no—
556C3⋊Dic3—22no—
557C3⋊Dic3—21no—
558C3⋊Dic3C22×Q812yes—
559C3⋊Dic3H(5,𝔽2)12yes—
560C3×Dic3—22no—
561C3×Dic3—24no—
562C3×Dic3—24no—
563C3×Dic3—22no—
564C3×Dic3C22×Q814yes—
565C2×#41—91no—
566C22×Q8—94no—
567C22×Q8—92no—
568C4⋊Q8—32no—
569C4⋊Q8—34no—
570C4⋊Q8—31no—
571C4⋊Q8—31no—
572C4⋊Q8—32no—
573C4⋊Q8—92no—
574C4⋊Q8—92no—
575C4⋊Q8—94no—
576C4⋊Q8—92no—
577C4⋊Q8—92no—
578C4⋊Q8—94no—
579C4⋊Q8—94no—
580C4⋊Q8—92no—
581C4⋊Q8—91no—
582C4⋊Q8—91no—
583#125—32no—
584#125—94no—
585#125—94no—
586#125—94no—
587#125—92no—
588#125—92no—
589C22⋊Q8—32no—
590C22⋊Q8—34no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—94no—
594C22⋊Q8—94no—
595C22⋊Q8—92no—
596C22⋊Q8—94no—
597C22⋊Q8—94no—
598C22⋊Q8—91no—
599C22⋊Q8—92no—
600C22⋊Q8—91no—
601C4×Q8—32no—
602C4×Q8—31no—
603C4×Q8—32no—
604C4×Q8—94no—
605C4×Q8—92no—
606C4×Q8—91no—
607C4×Q8—92no—
608C4×Q8—92no—
609C4×Q8—91no—
610C4×Q8D3211yescharacteristic
611C4×D4—31no—
612C4×D4—32no—
613C4×D4—94no—
614C4×D4—92no—
615C4×D4—92no—
616C4×D4—94no—
617C4×D4—91no—
618C4×D4—92no—
619#117—94no—
620#117—92no—
621#117—91no—
622#117—92no—
623C2×C4⋊C4—32no—
624C2×C4⋊C4—92no—
625C2×C4⋊C4—92no—
626C2×C4⋊C4—94no—
627C2×C4⋊C4—92no—
628C2×C42—92no—
629C2×C42—91no—
630C23×C3—32no—
631C22×D3—31no—
632C22×D3—31no—
633C22×D3—61no—
634C22×D3C23×D312yes—
635C3×Q8—22no—
636C3×Q8—22no—
637C3×Q8—34no—
638C3×Q8—42no—
639C3×Q8—122no—
640C3×Q8—122no—
641C3×Q8—124no—
642C3×D4—34no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—34no—
651C2×C3×C4—32no—
652C2×C3×C4—34no—
653C2×C3×C4—64no—
654C2×C3×C4—124no—
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657C2×C3×C4C23×D312yes—
658C2×C3×C4C23×D312yes—
659C2×C3×C4C23×D312yes—
660C2×C3×C4C23×D312yes—
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664C2×C3×C4C23×D311yescharacteristic
665#67—38no—
666C2×Dic3—31no—
667C2×Dic3—31no—
668C2×Dic3—31no—
669C2×Dic3—31no—
670C2×Dic3—38no—
671C2×Dic3—32no—
672C2×Dic3—32no—
673C2×Dic3—31no—
674C2×Dic3—31no—
675C2×Dic3—32no—
676C2×Dic3—32no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—62no—
681C2×Dic3—62no—
682C2×Dic3—64no—
683C2×Dic3—124no—
684C2×Dic3C23×D312yes—
685C2×Dic3C23×D312yes—
686C2×Dic3C23×D314yes—
687C2×Dic3C23×D314yes—
688C2×Dic3C23×D312yes—
689D12—38no—
690D12D3×Q814yescomplemented
691C4×D3—24no—
692C4×D3—38no—
693C4×D3—34no—
694C4×D3—34no—
695C4×D3—44no—
696C4×D3—64no—
697C4×D3—62no—
698C4×D3—62no—
699C4×D3—64no—
700C4×D3—62no—
701C4×D3—62no—
702C4×D3—122no—
703C4×D3—122no—
704C4×D3—124no—
705C4×D3—124no—
706C4×D3—124no—
707Dic6—44no—
708Dic6—42no—
709Dic6—42no—
710Dic6—68no—
711Dic6—68no—
712Dic6—64no—
713Dic6—64no—
714Dic6—62no—
715Dic6—62no—
716Dic6—124no—
717Dic6—122no—
718Dic6—124no—
719Dic6—124no—
720Dic6D3×Q814yescomplemented
721C2×C32C23×Q811yescharacteristic
722C2×C32C2×H(5,𝔽2)11yescharacteristic
723C2×C32C2×2−1+411yescharacteristic
724C3⋊D3—22no—
725C3×D3—24no—
726#41—98no—
727C2×Q8—31no—
728C2×Q8—32no—
729C2×Q8—34no—
730C2×Q8—32no—
731C2×Q8—94no—
732C2×Q8—94no—
733C2×Q8—91no—
734C2×Q8—92no—
735C2×Q8—368no—
736C2×Q8—364no—
737C2×Q8C2×D3211yescharacteristic
738C2×D4—31no—
739C2×D4—92no—
740C22×C4—32no—
741C22×C4—34no—
742C22×C4—94no—
743C22×C4—92no—
744C22×C4—92no—
745C22×C4—94no—
746C22×C4—91no—
747C22×C4—91no—
748C22×C4—91no—
749C4⋊C4—32no—
750C4⋊C4—34no—
751C4⋊C4—32no—
752C4⋊C4—32no—
753C4⋊C4—34no—
754C4⋊C4—32no—
755C4⋊C4—31no—
756C4⋊C4—32no—
757C4⋊C4—31no—
758C4⋊C4—34no—
759C4⋊C4—34no—
760C4⋊C4—94no—
761C4⋊C4—94no—
762C4⋊C4—94no—
763C4⋊C4—94no—
764C4⋊C4—92no—
765C4⋊C4—94no—
766C4⋊C4—94no—
767C4⋊C4—92no—
768C4⋊C4—91no—
769C4⋊C4—92no—
770C4⋊C4—92no—
771C4⋊C4—92no—
772C4⋊C4—92no—
773C4⋊C4—92no—
774C4⋊C4C2×D3211yescharacteristic
775C4⋊C4C2×D3212yes—
776C22⋊C4—32no—
777C22⋊C4—34no—
778C22⋊C4—92no—
779C22⋊C4—92no—
780C22⋊C4—94no—
781C22⋊C4—92no—
782C22⋊C4—92no—
783C42—32no—
784C42—34no—
785C42—92no—
786C42—92no—
787C42—94no—
788C42—91no—
789C42—91no—
790C42—91no—
791C42—92no—
792C42C2×D3211yescharacteristic
793C42C2×D3212yes—
794C22×C3—21no—
795C22×C3—34no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3C24×D311yescharacteristic
799C22×C3C24×D311yescharacteristic
800C2×D3—22no—
801C2×D3—22no—
802C2×D3—32no—
803C2×D3—32no—
804C2×D3—62no—
805C2×D3—61no—
806C2×D3—61no—
807C2×D3—61no—
808C2×D3—61no—
809C2×D3—121no—
810C2×D3—121no—
811C2×D3C2×D3×Q814yes—
812C3×C4—22no—
813C3×C4—22no—
814C3×C4—22no—
815C3×C4—21no—
816C3×C4—21no—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—22no—
820C3×C4—34no—
821C3×C4—42no—
822C3×C4—41no—
823C3×C4—42no—
824C3×C4—62no—
825C3×C4—64no—
826C3×C4—64no—
827C3×C4—62no—
828C3×C4C2×D3×Q812yes—
829C3×C4C2×D3×Q812yes—
830C3×C4#100712yes—
831C3×C4#101012yes—
832Dic3—22no—
833Dic3—24no—
834Dic3—22no—
835Dic3—24no—
836Dic3—32no—
837Dic3—32no—
838Dic3—32no—
839Dic3—32no—
840Dic3—62no—
841Dic3—62no—
842Dic3—62no—
843Dic3—61no—
844Dic3—62no—
845Dic3—61no—
846Dic3—62no—
847Dic3—62no—
848Dic3—122no—
849Dic3—122no—
850Dic3—121no—
851Dic3C2×D3×Q814yes—
852C32#350311yescharacteristic, complemented, Sylow
853C23—32no—
854C23—91no—
855Q8—22no—
856Q8—34no—
857Q8—124no—
858Q8—122no—
859Q8—122no—
860Q8—184no—
861Q8—188no—
862Q8—182no—
863Q8—364no—
864D4—34no—
865D4—98no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—34no—
869C2×C4—32no—
870C2×C4—34no—
871C2×C4—64no—
872C2×C4—98no—
873C2×C4—91no—
874C2×C4—91no—
875C2×C4—94no—
876C2×C4—92no—
877C2×C4—91no—
878C2×C4—92no—
879C2×C4—124no—
880C2×C4—182no—
881C2×C4—184no—
882C2×C4—182no—
883C2×C4—364no—
884C2×C4—364no—
885C2×C4C22×D3212yes—
886C2×C4C22×D3211yescharacteristic
887C2×C4C22×D3212yes—
888C2×C4C22×D3211yescharacteristic
889C2×C4C22×D3211yescharacteristic
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—64no—
894C2×C3C22×D3×Q811yescharacteristic
895C2×C3C22×D3×Q811yescharacteristic
896C2×C3C2×#100711yescharacteristic
897C2×C3C2×#101011yescharacteristic
898C2×C3D3×H(5,𝔽2)11yescharacteristic
899C2×C3D3×H(5,𝔽2)11yescharacteristic
900D3—24no—
901D3—62no—
902D3—62no—
903D3—122no—
904C22—34no—
905C22—62no—
906C22—62no—
907C22—92no—
908C22—181no—
909C22—181no—
910C22C23×D3211yescharacteristic
911C4—22no—
912C4—22no—
913C4—21no—
914C4—34no—
915C4—62no—
916C4—64no—
917C4—62no—
918C4—64no—
919C4—92no—
920C4—92no—
921C4—181no—
922C4—182no—
923C4—182no—
924C4#6429712yes—
925C4D32×Q812yes—
926C3—21no—
927C3#8692611yescharacteristic, complemented
928C3#8704111yescharacteristic, complemented
929C2—64no—
930C2—182no—
931C2C2×#6429711yescharacteristic
932C2C2×D32×Q811yescharacteristic
933C2#1059669211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×#3796C22
hypercenterC4×Q8D32
hypocenterC32#3503
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10596049C2semidirect
2. C3×#5579C2semidirect
3. C3×Q8×Dic6C2semidirect
4. #10595371C2semidirect
5. #10595367C2semidirect
6. #10594537C2semidirect
7. #10594391C2semidirect
8. #10594378C2semidirect
9. D3×#888C2semidirect
10. #10593956C2semidirect
11. #10593909C2semidirect
12. #10593904C2semidirect
15. #10593856C2semidirect
16. #10593855C2semidirect
17. #10593853C2semidirect
104. #5579D3semidirect
113. Q8×Dic6D3semidirect
141. #3796Q8semidirect
345. C4×C3⋊D3C2×Q8semidirect
353. C3×D12C2×Q8semidirect
359. C3×Dic6C2×Q8semidirect
362. #626C2×Q8semidirect
366. D3×Dic3C2×Q8semidirect
690. D12D3×Q8semidirect
720. Dic6D3×Q8semidirect
852. C32#3503semidirect
927. C3#86926semidirect
928. C3#87041semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105960492
C3×#55792
C3×Q8×Dic62
#105953712
#105953672
#105945372
#105943912
#105943782
D3×#8882
#105939562
#105939092
#105939042
#105938892
C4×#37962
#105938562
#105938552
#105938532
#870413
#869263